Mathematics of Discrete Structures for Computer Science

Deep learning on graphs has become one of the hottest topics in machine learning. The book consists of four parts to best accommodate our readers with diverse backgrounds and purposes of reading. Part 1 introduces basic concepts of graphs and deep learning; Part 2 discusses the most established methods from the basic to advanced settings; Part 3 presents the most typical applications including natural language processing, computer vision, data mining, biochemistry and healthcare; and Part 4 describes advances of methods and applications that tend to be important and promising for future research. The book is self-contained, making it accessible to a broader range of readers including (1) senior undergraduate and graduate students; (2) practitioners and project managers who want to adopt graph neural networks into their products and platforms; and (3) researchers without a computer science background who want to use graph neural networks to advance their disciplines.

Cummings/Worley's ORGANIZATION DEVELOPMENT AND CHANGE, 12th Edition, is the most widely-used textbook in the field. It blends rigor and relevance in a comprehensive and clear presentation. The authors work from a strong evidence-based foundation to describe, in practical terms, how behavioral science knowledge can be used to help organizations develop strategies, structures and processes for superior performance, sustainability and social outcomes.

The rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms are an important feature. Although other books cover parts of this material, none has a similarly wide scope. Ortrud R. Oellermann (Winnipeg), internationally recognised for her substantial contributions to structural graph theory, acted as academic consultant for this volume, helping shape its coverage of key topics. The result is a collection of thirteen expository chapters, each written by acknowledged experts. These contributions have been carefully edited to enhance readability and to standardise the chapter structure, terminology and notation throughout. An introductory chapter details the background material in graph theory and network flows and each chapter concludes with an extensive

Complex Analysis with Mathematica offers a way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos and advanced conformal mapping. A CD is included which contains a live version of the book: in particular all the Mathematica code enables the user to run computer experiments.

Neuronal dendritic trees are complex structures that endow the cell with powerful computing capabilities and allow for high neural interconnectivity. Studying the function of dendritic structures has

A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM)In recent years there has been increased interest in the nature and role of proof in mathematics education; with

A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM)In recent years there has been increased interest in the nature and role of proof in mathematics education; with

Technological artefacts and biological organisms 'evolve' by very similar processes of blind variation and selective retention. This analogy is explored systematically, for the first time, by a team of international experts from evolutionary biology, history and sociology of science and technology, cognitive and computer science, economics, psychology, education, cultural anthropology and research management. Do technological 'memes' play the role of genes? In what sense are novel inventions 'blind'? Does the element of design make them 'Lamarckian' rather than 'Darwinian'? Is the recombination of ideas the essence of technological creativity? Can invention be simulated computationally? What are the entities that actually evolve - artefacts, ideas or organisations? These are only some of the many questions stimulated and partially answered by this powerful metaphor. With its practical demonstration of the explanatory potential of 'evolutionary reasoning' in a well-defined context, this

Recent and ongoing developments in science and technology - such as the prevention and treatment of disease through genetics and the development of increasingly sophisticated computer systems with wide-ranging applications - hold out the promise of vastly improving the quality of human life, but they can also raise serious ethical, legal, and public policy questions. The thirteen essays in this volume address these questions and related issues from a variety of perspectives. Written by prominent philosophers, economists, and legal theorists, these essays offer valuable insights into the nature of scientific innovation and its implications for our social policies and practices.

This volume brings together scholars of Mediterranean archaeology, ancient history, and complexity science to advance theoretical approaches and analytical tools for studying maritime connectivity. For the coast-hugging populations of the ancient Mediterranean, mobility and exchange depended on a distinct environment and technological parameters that created diverse challenges and opportunities, making the modeling of maritime interaction a paramount concern for understanding cultural interaction more generally. Network-inspired metaphors have long been employed in discussions of this interaction, but increasing theoretical sophistication and advances in formal network analysis now offer opportunities to refine and test the dominant paradigm of connectivity. Extending from prehistory into the Byzantine period, the case studies here reveal the potential of such network approaches. Collectively they explore the social, economic, religious, and political structures that guided Mediterrane

This text introduces the basic equations of the theory of structures. Conventional presentations of these equations follow the ideas of elastic analysis, introduced nearly two hundred years ago. The book is written against the background of advances made in structural theory during the last fifty years, notably by the introduction of so-called plastic theory. The emphasis throughout is on the derivation and application of the structural equations, rather than on details of their solution (nowadays best done by computer), and the numerical examples are deliberately kept simple.

A text for a graduate course on linear system theory, with core material on the theory of time-varying linear systems in both continuous- and discrete-time and the time-invariant case. Chapters on sub

The mechanical properties of small volumes of materials such as thin films and patterned structures can be very different from the mechanical properties of those same materials in bulk. Many explanations of the mechanical behaviors of such small volumes have depended on simplified models of dislocation behavior. However, recent developments in dislocation modeling have made it possible to understand dislocation behavior in much more detail than before. A wide range of topics is presented in these proceedings, including mechanisms of plastic deformation in heteroepitaxial, multilayered and polycrystalline thin films, as well as three-dimensional mesostructures such as epitaxial islands, semiconducting devices and microcrystallites. Experimental, theoretical and numerical simulations are addressed. Topics include: dislocation and deformation mechanisms in thin metal films and multilayers; discrete dislocations - observations and simulations; dislocations and deformation mechanisms in thi

The new edition of a widely used introduction to game theory and its applications, with a focus on economics, business, and politics.This widely used introduction to game theory is rigorous but accessible, unique in its balance between the theoretical and the practical, with examples and applications following almost every theory-driven chapter. In recent years, game theory has become an important methodological tool for all fields of social sciences, biology and computer science. This second edition of Strategies and Games not only takes into account new game theoretical concepts and applications such as bargaining and matching, it also provides an array of chapters on game theory applied to the political arena. New examples, case studies, and applications relevant to a wide range of behavioral disciplines are now included. The authors map out alternate pathways through the book for instructors in economics, business, and political science. The book contains four parts: strategic form

In online computation a computer algorithm must decide how to act on incoming items of information without any knowledge of future inputs. How should it route the next telephone call? Where in memory should it store a just-closed record? This book provides an in-depth presentation of competitive analysis, an attractive framework within which such problems can be analyzed and solved. In this framework, the quality of an algorithm is measured relative to the best possible performance of an algorithm that has complete knowledge of the future. This methodology for the analysis of online decision making has become a standard approach in computer science. Starting with the basic definitions of the competitive analysis model, the authors present most of the essential techniques through various examples, some of which are among the central problems of the field, such as list accessing, paging in a virtual memory system, routing in a communication network, metrical task systems, k-server system

Featuring research from the 2017 research symposium of the Association for Women in Mathematics, this volume presents recent findings in pure mathematics and a range of advances and novel applications

This book is an introduction for readers interested in biological applications of mathematics and modeling in biology, showing how relatively simple mathematics can be applied to a variety of models.

Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an important discipline on its own. Acta Numerica surveys annually the most important developments in numerical analysis and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important developments in the subject in a manner accessible to the wider community of professionals with an interest in scientific computing.

Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an important discipline on its own. Acta Numerica surveys annually the most important developments in numerical analysis and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important developments in the subject in a manner accessible to the wider community of professionals with an interest in scientific computing.

Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an important discipline on its own. Acta Numerica surveys annually the most important developments in numerical analysis and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important developments in the subject in a manner accessible to the wider community of professionals with an interest in scientific computing.

Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an important discipline on its own. Acta Numerica surveys annually the most important developments in numerical analysis and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important developments in the subject in a manner accessible to the wider community of professionals with an interest in scientific computing.

Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an important discipline on its own. Acta Numerica surveys annually the most important developments in numerical analysis and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important developments in the subject in a manner accessible to the wider community of professionals with an interest in scientific computing.

Numerical analysis is the subject of applied mathematics concerned mainly with using computers in evaluating or approximating mathematical models. As such, it is crucial to all applications of mathematics in science and engineering, as well as being an important discipline on its own. Acta Numerica surveys annually the most important developments in numerical analysis and scientific computing. The subjects and authors of the substantive survey articles are chosen by a distinguished international editorial board so as to report the most important developments in the subject in a manner accessible to the wider community of professionals with an interest in scientific computing.

Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the cour

In-operation vibration monitoring for complex mechanical structures and rotating machines is of key importance in many industrial areas such as aeronautics (wings and other structures subject to stren

Quantum annealing is a new-generation tool of information technology, which helps in solving combinatorial optimization problems with high precision, based on the concepts of quantum statistical physics. Detailed discussion on quantum spin glasses and its application in solving combinatorial optimization problems is required for better understanding of quantum annealing concepts. Fulfilling this requirement, the book highlights recent development in quantum spin glasses including Nishimori line, replica method and quantum annealing methods along with the essential principles. Separate chapters on simulated annealing, quantum dynamics and classical spin models are provided for enhanced learning. Important topics including adiabatic quantum computers and quenching dynamics are discussed in detail. This text will be useful for students of quantum computation, quantum information, statistical physics and computer science.

Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematic

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practising engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dy

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practising engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dy

Markov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject by first developing the theory of Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and graduates. The authors then introduce semi-Markov chains and hidden semi-Markov chains, before developing related estimation and filtering results. Genomics applications are modelled by discrete observations of these hidden semi-Markov chains. This book contains new results and previously unpublished material not available elsewhere. The approach is rigorous and focused on applications.

Within the rapidly-growing arena of 'virtual worlds', such as Massively Multiplayer Online Games (MMOs), individuals behave in particular ways, influence one another, and develop complex relationships. This setting can be a useful tool for modeling complex social systems, cognitive factors, and interactions between groups and within organizations. To study these worlds effectively requires a cross-disciplinary approach that integrates social science theories with big data analytics. This broad-based book offers a comprehensive and holistic perspective on the field. It brings together research findings from an international team of experts in computer science (artificial intelligence, game design, and social computing), psychology, and the social sciences to help researchers and practitioners better understand the fundamental processes underpinning social behavior in virtual worlds such as World of Warcraft, Rift, Eve Online, and Travian.

The interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics. Bringing together contributions from a 2017 conference at the University of Potsdam, this volume focuses on global effects of local properties. Exploring the similarities and differences between the discrete and the continuous settings is of great interest to both researchers and graduate students in geometric analysis. The range of survey articles presented in this volume give an expository overview of various topics, including curvature, the effects of geometry on the spectrum, geometric group theory, and spectral theory of Laplacian and Schrödinger operators. Also included are shorter articles focusing on specific techniques and problems, allowing the reader to get to the heart of several key topics.

This collection of contributions surveys the state-of-the-art in computer applications for graphics in art, animation and design. It provides an integrative view of the technological, computer-related

This is an introduction to the dynamics of fluids at small scales, the physical and mathematical underpinnings of Brownian motion, and the application of these subjects to the dynamics and flow of complex fluids such as colloidal suspensions and polymer solutions. It brings together continuum mechanics, statistical mechanics, polymer and colloid science, and various branches of applied mathematics, in a self-contained and integrated treatment that provides a foundation for understanding complex fluids, with a strong emphasis on fluid dynamics. Students and researchers will find that this book is extensively cross-referenced to illustrate connections between different aspects of the field. Its focus on fundamental principles and theoretical approaches provides the necessary groundwork for research in the dynamics of flowing complex fluids.

This is an introduction to the dynamics of fluids at small scales, the physical and mathematical underpinnings of Brownian motion, and the application of these subjects to the dynamics and flow of complex fluids such as colloidal suspensions and polymer solutions. It brings together continuum mechanics, statistical mechanics, polymer and colloid science, and various branches of applied mathematics, in a self-contained and integrated treatment that provides a foundation for understanding complex fluids, with a strong emphasis on fluid dynamics. Students and researchers will find that this book is extensively cross-referenced to illustrate connections between different aspects of the field. Its focus on fundamental principles and theoretical approaches provides the necessary groundwork for research in the dynamics of flowing complex fluids.

Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early so

This new book for mathematics teachers helps them gain an appreciation of geometry and its importance in the history and development of mathematics. The material is presented in three parts. The firs

This book invites the reader to understand our Universe, not just marvel at it. From the clock-like motions of the planets to the catastrophic collapse of a star into a black hole, gravity controls the Universe. Gravity is central to modern physics, helping to answer the deepest questions about the nature of time, the origin of the Universe and the unification of the forces of nature. Linking key experiments and observations through careful physical reasoning, the author builds the reader's insight step-by-step from simple but profound facts about gravity on Earth to the frontiers of research. Topics covered include the nature of stars and galaxies, the mysteries of dark matter and dark energy, black holes, gravitational waves, inflation and the Big Bang. Suitable for general readers and for undergraduate courses, the treatment uses only high-school level mathematics, supplemented by optional computer programs, to explain the laws of physics governing gravity.

The aim of this book is to expand and improve upon the existing knowledge on discrete-time 1-bit look-ahead sigma-delta modulation in general, and to come to a solution for the above mentioned specifi

“Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.” From the Principles for School Mathematics of NCTM standards, copyright NCTM